In November 2003, the now-most-distant-known object in the solar system was discovered by observation with a telescope on Mt. Palomar. This object, known as Sedna, is approximately 1700 km in diameter, takes about 10,500 years to orbit our sun, and reaches a maximum speed of 4.64 km/s. Calculations of its complete path, based on several measurements of its position, indicate that its orbit is highly elliptical, varying from 76 AU to 942 AU in its distance from the sun, where AU is the astronomical unit, which is the average distance of the earth from the sun (1.50 × 10⁸ km).

(a) What is Sedna’s minimum speed?

(b) At what points in its orbit do its maximum and minimum speeds occur?

(c) What is the ratio of Sedna’s maximum kinetic energy to its minimum kinetic energy?